Pith Number

pith:OBJQKZP3

pith:2015:OBJQKZP3DT2AJRIPPZS3E4MAE7

not attested not anchored not stored refs pending

Two Generator groups acting on the complex hyperbolic plane

Pierre Will

arxiv:1510.01500 v1 · 2015-10-06 · math.GT

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{OBJQKZP3DT2AJRIPPZS3E4MAE7}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Receipt and verification

First computed	2026-05-18T01:30:56.794112Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

70530565fb1cf404c50f7e65b2718027fbdb0b5fbd681897898438fdc114f59b

Aliases

arxiv: 1510.01500 · arxiv_version: 1510.01500v1 · doi: 10.48550/arxiv.1510.01500 · pith_short_12: OBJQKZP3DT2A · pith_short_16: OBJQKZP3DT2AJRIP · pith_short_8: OBJQKZP3

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/OBJQKZP3DT2AJRIPPZS3E4MAE7 \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 70530565fb1cf404c50f7e65b2718027fbdb0b5fbd681897898438fdc114f59b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9904705d2ecf4bb749c61aac5392b0a96cb8dea4e0680633ee6a2936969657b1",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2015-10-06T09:41:10Z",
    "title_canon_sha256": "b4ccc57908ea09a62d149fbd4c1f56e348173ff3f54e60fb5be804f5b5ea07a6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1510.01500",
    "kind": "arxiv",
    "version": 1
  }
}